Gravity is the force of inherent natural attraction between two massive bodies. The magnitude of the gravitational force is directly related to the mass of the bodies and is inversely related to the square of the distance between centers of mass of the two attracted bodies.
Gravity is measured as acceleration, g, usually as a vertical vector component. The freefall acceleration, g, of an object near the surface of the earth is given to a first approximation by the gravitational attraction of a point with the mass of the entire earth, Me, located at the center of the earth, a distance, Re, from the surface of the earth. This nominal gravity value, g=G×Me/Re2, is about 9.8 m/s2. Thus, the freefall acceleration due to gravity near the earth's surface of an object having a small mass compared to the mass of the earth is about 9.8 m/s2. The common unit of measurement for gravity is the “Galileo” (Gal), which is a unit of acceleration defined as 1 cm/s2. One Gal generally approximates 1/1000 (10−3) of the force of gravity at the earth's surface. An instrument used to measure gravity is called a “gravimeter.”
The most accurate gravimeters are absolute gravimeters. Interferometric absolute gravimeters usually use a freely falling test mass and a laser or single-frequency light beam which reflects from the freely falling test mass. The reflected light beam is combined with a reference light beam to develop interference fringes. Interference fringes are instances where the amplitude or intensity of the reflected and reference light beams add together to create increased intensity, separated by instances where the two beams cancel or create diminished intensity.
Fringes occur on a periodic basis depending upon the change in the optical path length of the reflected beam relative to the optical path length of the reference beam. One fringe occurs whenever the optical path difference between the reflected and reference beams changes by the wavelength of the light in the two beams. When a test mass that is part of the beam path falls freely, the freefall movement of the test mass typically changes the path length by twice the amount of movement because both the entry and exit of the beam path are changed. In this circumstance, a fringe typically occurs when the test mass moves by one-half of a wavelength. The fringes taken together as a set comprise a record of the distance that the freely falling test mass moves.
Because the path length of the reflected beam changes as it is reflected from the freely falling test mass, and because the freefall movement of the test mass is established by gravity, the occurrence and timing of the resulting interference fringes defines the characteristic of gravity. The use of optical fringe interferometry to measure gravity characteristics is well-known. An example of an interferometric absolute gravimeter is described in U.S. Pat. No. 5,351,122.
In addition to measuring gravity, light beam interferometry has also been applied to measure a gradient of gravity. A gradient of gravity is the rate at which gravity changes in a certain direction and over a certain distance. A gravity gradient is therefore the change or first derivative of the gravity value over distance. An instrument used to measure a gradient of gravity is called a “gradiometer.”
Gravity gradients from subsurface density anomalies, such as a pool of liquid petroleum encased within an earth formation, narrow seams or “tubes” of high density geological materials such as diamonds or cobalt, or voids in a geographical formation caused by a tunnel or cavern, are most measurable within a relatively short near-field distance, typically within a few hundred meters. Such near-field density anomalies affect the local value of gravity, g, at a level of about 1 part per million ( 1/106), and in some cases 1 part per billion ( 1/109). The large background of the earth's gravity requires that any direct gravity measurement to detect such subsurface anomalies have a very large dynamic range of parts per billion, otherwise direct gravity measurements will not be useful for locating and detecting such subsurface density anomalies. It is difficult to make gravimeters with such levels of extremely high precision, so gradiometers are used to cancel the large effect of the earth's gravity while preserving the ability to detect nearby density anomalies. However, gravity measurements using gravimeters are required to detect and evaluate medium-field and far-field density anomalies.
The vertical gravity gradient of the earth is relatively much smaller in comparison to the vertical gravity gradient caused by nearby mass or density anomalies. The vertical gravity gradient is typically measured in terms of a unit called the Eotvos unit, E, given by 10−9/s2. The vertical gravity gradient of the entire earth is typically about 3000E. Typical nearby mass anomalies can affect the vertical gravity gradient at a level of about 1E or more. Thus, the contrast of the vertical gravity gradient caused by nearby mass anomalies to the earth's vertical gravity gradient is about 300,000 (3×105) times larger than for the gravity value itself. This means that a vertical gradiometer can have 3×105 times less precision than a gravimeter and still be used effectively to detect or locate nearby mass or density anomalies. However, even though effective with less precision than a gravimeter, a gradiometer is still subject to erroneous measurements from the occurrence of anomalous fringes.
Each gravimeter and gradiometer which uses a freely falling test mass is subject to naturally-occurring and man-made vibrations and other physical perturbations. These vibrations and perturbations cause minute changes in the path length of the reflected and reference light beams, causing interference fringes which are not related to the gravity characteristic measured but instead are related to the noise arising from the aberrant vibrations and other physical perturbations. Such anomalous interference fringes reduce the accuracy of the measurement of the gravity characteristic and enhance the potential for errors. These types of errors are not typically subject to common mode rejection because the errors uniquely affect some singular aspect of the light path or the gradiometer or gravimeter. The inability to achieve effective common mode rejection makes the measurement of a gravity characteristic error-prone, particularly in vibration-prone or perturbation-prone environments.
One of several possible causes of inaccuracies in the measurements from interferometric gravity characteristic devices is the random and unintended rotation or tilting of the test mass during freefall. The test mass is prone to rotate during freefall due to vibrations or perturbations of the gravimeter or gradiometer at the moment that the test mass is released or launched for freefall. The rotation of the test mass changes the length of the light beam path and that change is unrelated to the influence of gravity on the test mass. The interference fringes therefore distort or mask the true influence of gravity on the freefalling test mass, and this distortion diminishes the accuracy of the measured gravity characteristic. Even a very slight amount of angular rotation or tilting of the test mass during freefall is enough to cause a significant error in measurement.
Prior known attempts at avoiding angular rotation or tilting of the test mass during freefall have focused principally on attempting to mechanically isolate the test mass from the adverse influences of external vibrations and perturbations, and on attempting to mechanically release the test mass for freefall without inducing tilting or angular rotation. However, such mechanical measures have not proved entirely satisfactory in eliminating rotation or tilting of the test mass during freefall, and consequently anomalous interference fringes have occurred and degraded the quality of the gravity characteristic measurement.